A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form ω is ∂∂-closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a 2. n-dimensional SKT Lie algebra g and using a Hermitian flat connection on g we construct a 4. n-dimensional SKT Lie algebra. We apply this method to some 4-dimensional SKT Lie algebras. Moreover, we classify symplectic forms taming complex structures on 4-dimensional Lie algebras.
Special Hermitian metrics and Lie groups
ENRIETTI, NICOLA;FINO, Anna Maria
2011-01-01
Abstract
A Hermitian metric on a complex manifold is called strong Kähler with torsion (SKT) if its fundamental 2-form ω is ∂∂-closed. We review some properties of strong KT metrics also in relation with symplectic forms taming complex structures. Starting from a 2. n-dimensional SKT Lie algebra g and using a Hermitian flat connection on g we construct a 4. n-dimensional SKT Lie algebra. We apply this method to some 4-dimensional SKT Lie algebras. Moreover, we classify symplectic forms taming complex structures on 4-dimensional Lie algebras.
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